A bipartisan group of senators on Thursday introduced an overhaul to foreign lobbying rules, while a similar, once fast-moving measure appears temporarily stalled in the House amid pressure from outside interests.

The new bill from Texas Republican John Cornyn and California Democrat Dianne Feinstein indicates that momentum to revamp foreign lobbying disclosures persists as the Russia probe has kept concerns about international influences in the spotlight. But opposition remains.

Representatives of foreign-owned businesses and multinational nonprofit organizations say they do not want the stigma of being defined as foreign agents. They are pushing for changes to legislation that swiftly passed the House Judiciary Committee in January but has not yet been scheduled for floor action.

A companion bill from Iowa GOP Sen. Charles E. Grassley appears in limbo at Foreign Relations, the committee of jurisdiction. A committee aide said the panel was “carefully reviewing the legislation.”

Outside proponents of the measure say they, too, are making the rounds on Capitol Hill to build momentum for action.

U.S. subsidiaries of foreign-owned corporations say they are most concerned that the bills would reverse a long-standing exemption and require their lobbyists to register under the Foreign Agents Registration Act. The 1938 law has gained new fame with the indictments of former lobbyists Rick Gates and Paul Manafort, who worked on President Donald Trump’s campaign, for allegedly failing to comply with it. The charges stem from the investigation of special counsel Robert S. Mueller III into foreign interference in the 2016 presidential election.

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Unwanted label

Under current law, lobbyists for foreign corporations and their U.S. affiliates may register under less burdensome congressional lobbying disclosure rules.

“To label them as a foreign agent would have a chilling effect on their interest in talking to their elected representatives and hamper their ability to communicate their policy concerns,” said Nancy McLernon, president of the Organization for International Investment, whose members are international companies with U.S. operations such as Nestle, BASF and Siemens.

McLernon said that together her member companies employ nearly 7 million people in the United States and that her group has taken its concerns to the bill’s chief House sponsor, Louisiana Republican Mike Johnson.

Registered foreign agents, which include many of Washington’s high-profile law and lobbying firms and former members of Congress from both political parties, are required by law to disclose much more about their lobbying — such as which congressional offices they meet with — than what is required under congressional lobbying regulations. Lobbyists file congressional lobbying reports quarterly with the House and Senate, while foreign agents file semi-annual reports to the Justice Department’s FARA unit.

“Our concern is that being identified as a foreign agent is certainly pejorative,” McLernon said. “We’ve had very constructive conversations with Congressman Johnson.”

Johnson’s office did not provide a comment about the current status of his bill. During the January markup, he said: “One of the worst kept secrets in Washington is how frequently lobbyists violate our foreign registration laws by accepting millions of dollars from foreign principals without disclosing a thing about those relationships.”

Robert Kelner, a partner at Covington & Burling and an expert on FARA, said the bills take a “blunt” approach to foreign lobbying that could inadvertently sweep in even U.S.-based companies as foreign agents. Kelner represents Michael Flynn, a former Trump national security adviser who has pleaded guilty in the Mueller probe.

Lax enforcement

The Justice Department’s own inspector general issued a report in 2016 calling enforcement of the law lax. The Johnson and Grassley bills would give the FARA unit new subpoena-like authority, another point of controversy for Democratic lawmakers who say they are reluctant to give the Trump administration’s DOJ more power.

It was during the Mueller investigation that previously unregistered foreign lobbying came to light. Lobbying firms that worked with Manafort on a Ukrainian client — the Podesta Group, which collapsed last year, and Mercury LLC — subsequently filed retroactive disclosures.

The Johnson-Grassley bills have the support of watchdog groups such as Common Cause, Issue One and Public Citizen.

Public Citizen’s Craig Holman said he’s been “spending a great deal of my time lobbying on both bills.”

He has been meeting with Democrats on the Senate Foreign Relations panel, he said, adding that they are reluctant to sign on to the measure because of arguments from the International Center for Not-for-Profit Law, which has concerns about changes to the system and the underlying law itself.

“We do think that before you can increase enforcement of the act, you need to fix the act,” said Nick Robinson the center’s legal adviser for U.S. programs. “It’s 80 years old now. It is far too broad and sweeping and captures all sort of nonprofit organizations that I don’t think anyone intended it to catch.”

“It should be about agents of foreign governments,” Robinson added.

The European Centre for a Modern Ukraine, the client of Manafort and the two lobbying firms, was a nonprofit organization reportedly controlled by Ukraine’s former president Viktor Yanukovych.

Who’s a foreign agent?

Still, Congress should spell out the definitions of the foreign agents law, Robinson said, adding that his group’s goal is not to abolish FARA.

Public Citizen’s Holman said he is lobbying to end the exemption for foreign corporations under the law, something he believes made it easier for Manafort’s team to skirt the disclosures before the special counsel investigation.

“It’s so easy to hide behind representing some sort of U.S. subsidiary of a corporation or a nonprofit,” Holman said.

Despite the competing lobbying campaigns over the measures, Holman said he still sees an overhaul to the foreign lobbying law as a doable endeavor this year.